Model matching level control for a coupled tanks system using time-scale separation technique

The problem of a level control system design for a specific connection of two tanks is discussed. We compare two algorithms for the first tank: a nonlinear feedback linearization algorthm and one based on a time-scale separation. The second technique leads to a PI controller for the level control in the first tank and either a single loop PID or a cascade of P/PI controllers for the level control in the second tank. A design methodology based on the time-scale separation technique is proposed in which controller parameters are selected such that fast and slow modes are induced in the closed-loop system. Hence, the singular perturbations method is used to analyze the closed-loop system properties. A particular feature of the considered two tanks connection is that its high frequency gain tends to infinity when the system attains equilibrium. Therefore, the fast-motion transients are analyzed based on Popov absolute stability criterion in presence of a sector-like condition in control. Numerical simulations confirm robustness with regard to plant parameters and external disturbances.